Susceptible
Students without the means to independently fund higher education.
Computational research · Mathematical modeling
Modeling the multi-stage dynamics of student debt
An interactive implementation of an SEIR-inspired system that reframes debt as a progression through four population states—from financial vulnerability to repayment.
The model
Four states, one evolving system
The research adapts the structure of an epidemiological SEIR model to represent stages in a student borrower's financial journey.
Exposed
Borrowers who have entered the student-loan system.
Excessive debt
Borrowers experiencing a financially burdensome level of debt.
Recovered
Borrowers who have completed repayment and exited the debt system.
Interactive experiment
Test the one-stage model
Change a transition rate, run the simulation, and compare how the timing and scale of debt burden respond.
Population trajectories
Proportion of the modeled population over time
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Under the hood
From equations to an explorable interface
One-stage differential system
dS/dt = −βSI
dE/dt = βSI − σE
dI/dt = σE − γI
dR/dt = γI
The implementation evaluates these coupled equations with a fourth-order Runge–Kutta solver while preserving a normalized population.
Translate
Convert the mathematical state transitions into testable JavaScript functions.
Simulate
Advance the system in small time steps and capture every population trajectory.
Communicate
Turn model output into an interactive chart and decision-friendly summary metrics.
Research context
A foundation for deeper analysis
The broader research extends this one-stage demonstration into multi-stage exposure models, reproduction-number analysis, vital dynamics, parameter estimation, and potential work with real-world data.